Conic Sections: Parabolas — Test Answers

Which graph represents the equation x2 = 8y?

Two circles are concentric if they have the same center.

A parabola has a vertex at the origin. The focus of the parabola is located at (–2,0).

On a coordinate plane, a parabola opens to the left. It has a vertex at (0, 0), a focus at (negative 2, 0), and a directrix at x = 2.

Samara is adjusting a satellite because she finds it is not focusing the incoming radio waves perfectly. The shape of her satellite can be modeled by where x and y are modeled in inches. She realizes that the static is a result of the feed antenna shifting slightly off the focus point. What is the focus point of the satellite?

Which is the standard form of the equation of the parabola that has a vertex of (–4, –3) and a directrix of x = 2?

Rene is designing a satellite that is the shape of a parabola that opens upward with a diameter of 8 in. and a depth of 2 in. The feed antenna focuses the incoming radio waves. At what point should the feed antenna be placed?

A parabola and its directrix are shown on the graph.

Gabriella is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by where x and y are measured in inches. Where should she place the bulb to ensure a perfect beam of light?

What is the center of a circle represented by the equation (x+9)2+(y−6)2=102?

Which equation represents the general form a circle with a center at (–2, –3) and a diameter of 8 units?

What is the radius of a circle whose equation is (x – 7)2 + (y – 10)2 = 4?

What is the center of a circle represented by the equation (x−5)2+(y+6)2=42?

What is the radius of a circle whose equation is x2+y2+8x−6y+21=0?